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Year 8

8.01 Areas of special quadrilaterals

Worksheet
Parallelograms
1

The given parallelogram is formed into a rectangle:

a

Find the area of the rectangle.

b

Hence, find the area of the parallelogram.

2

The given parallelogram is formed into a rectangle:

a

Find an expression for the area of the rectangle in terms of b and h.

b

Hence, find an expression for the area of the parallelogram in terms of b and h.

3

Find the area of the following parallelograms:

a
b
c
d
4

Determine whether the following pairs of values could be the dimensions of a parallelogram with an area of 70 \,\text{mm}^2.

a

Base =10 \,\text{mm}, Height =7 \,\text{mm}

b

Base =7 \,\text{mm}, Height =10 \,\text{mm}

c

Base =1 \,\text{mm}, Height =70 \,\text{mm}

d

Base =2 \,\text{mm}, Height =70 \,\text{mm}

Trapeziums
5

The given trapezium is split into a rectangle and a right-angled triangle:

a

Find the area of the rectangle.

b

Find the area of the triangle.

c

Hence, find the area of the trapezium.

6

The given trapezium is formed into a rectangle:

a

Find the length, l, of the rectangle.

b

Hence, find the area of the trapezium.

7

Two identical trapezia are put together to make a parallelogram:

a

Find the area of the entire parallelogram.

b

Find the area of one of the trapezia.

8

Two identical trapezia are put together to make a rectangle:

a

Find the area of the entire rectangle.

b

Find the area of one of the trapezia.

9

Two identical trapezia are put together to make a parallelogram:

a

Find an expression for the area of the entire parallelogram in terms of a, b and h.

b

Find an expression for the area of one trapezia in terms of a, b and h.

10

Find the area of the following trapeziums:

a
b
c
d
e
f
Rhombuses
11

The given rhombus can be split into two triangles:

a

Find the area of one triangle.

b

Hence, find the area of the rhombus.

12

The given rhombus is formed into a rectangle:

a

Find the length of the rectangle in terms of y.

b

Find the width of the rectangle in terms of x.

c

Find the area of the rectangle in terms of x and y.

d

Hence, find the area of the rhombus in terms of x and y.

13

Find the area of the following rhombuses:

a
b
c
d
e
f
14

Determine whether the following pairs of values could be the diagonal lengths, x and y of a rhombus with an area of 9 \,\text{m}^2.

a

x = 2 \,\text{m} and y = 9 \,\text{m}.

b

x = 6 \,\text{m} and y = 3 \,\text{m}.

c

x = 12 \,\text{m} and y = 3 \,\text{m}.

d

x = 6 \,\text{m} and y = 6 \,\text{m}.

Kites
15

The given kite can be split into two triangles:

a

Find the area of one of the triangles.

b

Hence, find the area of the kite.

16

The given kite is formed into a rectangle:

a

Find the length of the rectangle.

b

Find the width of the rectangle.

c

Hence, find the area of the kite.

17

The given kite is formed into a rectangle:

a

Find the length of the rectangle in terms of y.

b

Find the width of the rectangle in terms of x.

c

Find the area of the rectangle in terms of x and y.

d

Hence, find the area of the kite in terms of x and y.

18

Find the area of the following kites:

a
b
c
d
e
f
Mixed areas
19

Find the area of the following quadrilaterals:

a
b
c
d
e
f
g
h
i
j
Missing lengths
20

For each of the following rhombuses, find the value of the pronumeral:

a

A = 64 \text{ cm}^{2}

b

A = 128 \text{ cm}^{2}

21

Rhombus ABCD has an area of \\ A = 55\,\text{cm}^2:

Given the diagonal BD = 11 \,\text{cm}, and \\ AC = x \,\text{cm}, find the value of x.

22

Rhombus ABCD has an area of 13 \text{ cm}^{2}:

If diagonal AC = 2, and diagonal BD = y, find the value of y.

23

The following kite has an area of 48 \,\text{cm}^2. The length of one of its diagonals is 12 \,\text{cm}:

Find the length of the other diagonal, k.

24

For each of the following kites, find the value of k:

a

A = 15 \text{ cm}^{2}

b

A = 22.5 \text{ cm}^{2}

c

A = 56 \text{ cm}^{2}

d

A = 137.5 \text{ cm}^{2}

25

For each of the following trapezia, find the value of the pronumeral:

a

A = 42 \,\text{mm}^2

b

A = 36 \text{ cm}^{2}

c

A = 20 \text{ m}^{2}

d

A = 24 \text{ cm}^{2}

26

Find the value of x if the area of the trapezium shown is 65 \text{ cm}^{2}:

27

Find the perpendicular height, h, of a parallelogram that has an area of 45 \,\text{cm}^2 and a base of 5 \,\text{cm}.

28

Find the base length, b, of a parallelogram that has an area of \, 216 \,\text{mm}^2 and a perpendicular height of 12 \,\text{mm}.

29

The area of a kite is 640 \text{ cm}^{2} and one of the diagonals is 59 \text{ cm}. If the length of the other diagonal is y \text{ cm}, find the value of y, rounded to two decimal places.

30

Complete the table of base and height measurements for three parallelograms that all have an area of 24 \,\text{m}^2:

\text{Area}\, (\text{m}^2)\text{Base} \, (\text{m})\text{Height}\, (\text{m})
248
2412
246
31

Complete the table og the lengths of diagonal x and diagonal y for three kites that all have an area of 36 \,\text{mm}^2:

\text{Area} \ (\text{mm}^2) \text{Diagonal}, x \ (\text{mm})\text{Diagonal}, y \ (\text{mm})
3618
3624
3612
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